Malaysian Journal of Mathematical Sciences, February 2016, Vol. 10(S)
Special Issue: The 3rd International Conference on Mathematical Applications in Engineering 2014 (ICMAE'14)
$R$-Majorizing Quadratic Stochastic Operators: Examples on 2D Simplex
Saburov, M. and Yusof, N. A.
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
A vector majorization is a preorder of dispersion for vectors with the same length and same sum of components. The vector majorization can be viewed as a preorder of distance from a uniform vector. A preorder of distance from any fixed non-uniform vector of positive components, so-called $r$-majorization, is a generalization of usual vector majorization. In this paper, a new class of mappings so-called $r$-majorizing quadratic stochastic operators was introduced. The $r$-majorizing quadratic stochastic operator is a generalization of a quadratic doubly stochastic operator. Some relevant examples are provided. Moreover, the dynamics of some non-scrambling $r$-majorizing quadratic stochastic operators are studied.
Keywords: $R$-majorization, quadratic stochastic operators, scrambling matrix
